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Reworked azimuthal projections

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ClemensFischer 2026-01-19 21:38:18 +01:00
parent 19cba8978b
commit 2c9e478095
6 changed files with 117 additions and 107 deletions
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43
MapControl/Shared/AzimuthalEquidistantProjection.cs
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@ -11,7 +11,7 @@ namespace MapControl
/// Spherical Azimuthal Equidistant Projection - No standard CRS identifier.
/// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/publication/pp1395), p.195-197.
/// </summary>
public class AzimuthalEquidistantProjection : MapProjection
public class AzimuthalEquidistantProjection : AzimuthalProjection
{
public const string DefaultCrsId = "AUTO2:97003"; // proprietary CRS identifier
@ -22,38 +22,43 @@ namespace MapControl
public AzimuthalEquidistantProjection(string crsId)
{
Type = MapProjectionType.Azimuthal;
CrsId = crsId;
}
public double EarthRadius { get; set; } = Wgs84MeanRadius;
public override Point RelativeScale(double latitude, double longitude)
{
(var cosC, var _, var _) = GetPointValues(latitude, longitude);
var k = 1d;
if (cosC < 1d)
{
var c = Math.Acos(cosC);
k = c / Math.Sin(c); // p.195 (25-2)
}
return new Point(k, k);
}
public override Point? LocationToMap(double latitude, double longitude)
{
if (Center.Equals(latitude, longitude))
(var cosC, var x, var y) = GetPointValues(latitude, longitude);
var k = 1d;
if (cosC < 1d)
{
return new Point();
var c = Math.Acos(cosC);
k = c / Math.Sin(c); // p.195 (25-2)
}
Center.GetAzimuthDistance(latitude, longitude, out double azimuth, out double distance);
var mapDistance = distance * EarthRadius;
return new Point(mapDistance * Math.Sin(azimuth), mapDistance * Math.Cos(azimuth));
return new Point(EarthRadius * k * x, EarthRadius * k * y); // p.195 (22-4/5)
}
public override Location MapToLocation(double x, double y)
{
if (x == 0d && y == 0d)
{
return new Location(Center.Latitude, Center.Longitude);
}
var rho = Math.Sqrt(x * x + y * y);
var c = rho / EarthRadius; // p.196 (25-15)
var azimuth = Math.Atan2(x, y);
var mapDistance = Math.Sqrt(x * x + y * y);
var distance = mapDistance / EarthRadius;
return Center.GetLocation(azimuth, distance);
return GetLocation(x, y, rho, Math.Sin(c));
}
}
}

47
MapControl/Shared/AzimuthalProjection.cs Normal file
View file

@ -0,0 +1,47 @@
using System;
namespace MapControl
{
/// <summary>
/// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/publication/pp1395).
/// </summary>
public abstract class AzimuthalProjection : MapProjection
{
protected AzimuthalProjection()
{
Type = MapProjectionType.Azimuthal;
}
public double EarthRadius { get; set; } = Wgs84MeanRadius;
protected (double, double, double) GetPointValues(double latitude, double longitude)
{
var phi = latitude * Math.PI / 180d;
var phi1 = Center.Latitude * Math.PI / 180d;
var dLambda = (longitude - Center.Longitude) * Math.PI / 180d; // λ - λ0
var cosPhi = Math.Cos(phi);
var sinPhi = Math.Sin(phi);
var cosPhi1 = Math.Cos(phi1);
var sinPhi1 = Math.Sin(phi1);
var cosLambda = Math.Cos(dLambda);
var sinLambda = Math.Sin(dLambda);
var cosC = sinPhi1 * sinPhi + cosPhi1 * cosPhi * cosLambda; // (5-3)
var x = cosPhi * sinLambda;
var y = cosPhi1 * sinPhi - sinPhi1 * cosPhi * cosLambda;
return (cosC, x, y);
}
protected Location GetLocation(double x, double y, double rho, double sinC)
{
var cosC = Math.Sqrt(1d - sinC * sinC);
var phi1 = Center.Latitude * Math.PI / 180d;
var cosPhi1 = Math.Cos(phi1);
var sinPhi1 = Math.Sin(phi1);
var phi = Math.Asin(cosC * sinPhi1 + y * sinC * cosPhi1 / rho); // (20-14)
var dLambda = Math.Atan2(x * sinC, rho * cosPhi1 * cosC - y * sinPhi1 * sinC); // (20-15), λ - λ0
return new Location(phi * 180d / Math.PI, dLambda * 180d / Math.PI + Center.Longitude);
}
}
}

37
MapControl/Shared/GnomonicProjection.cs
View file

@ -11,7 +11,7 @@ namespace MapControl
/// Spherical Gnomonic Projection - AUTO2:97001.
/// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/publication/pp1395), p.165-167.
/// </summary>
public class GnomonicProjection : MapProjection
public class GnomonicProjection : AzimuthalProjection
{
public const string DefaultCrsId = "AUTO2:97001"; // GeoServer non-standard CRS identifier
@ -22,40 +22,37 @@ namespace MapControl
public GnomonicProjection(string crsId)
{
Type = MapProjectionType.Azimuthal;
CrsId = crsId;
}
public double EarthRadius { get; set; } = Wgs84MeanRadius;
public override Point RelativeScale(double latitude, double longitude)
{
(var cosC, var _, var _) = GetPointValues(latitude, longitude);
var h = 1d / (cosC * cosC); // p.165 (22-2)
return new Point(h, h); // TODO: rotate
}
public override Point? LocationToMap(double latitude, double longitude)
{
if (Center.Equals(latitude, longitude))
(var cosC, var x, var y) = GetPointValues(latitude, longitude);
if (cosC <= 0d)
{
return new Point();
return null;
}
Center.GetAzimuthDistance(latitude, longitude, out double azimuth, out double distance);
var k = 1d / cosC; // p.165 (22-3)
var mapDistance = distance < Math.PI / 2d
? Math.Tan(distance) * EarthRadius
: double.PositiveInfinity;
return new Point(mapDistance * Math.Sin(azimuth), mapDistance * Math.Cos(azimuth));
return new Point(EarthRadius * k * x, EarthRadius * k * y); // p.165 (22-4/5)
}
public override Location MapToLocation(double x, double y)
{
if (x == 0d && y == 0d)
{
return new Location(Center.Latitude, Center.Longitude);
}
var rho = Math.Sqrt(x * x + y * y);
var c = Math.Atan(rho / EarthRadius); // p.167 (22-16)
var azimuth = Math.Atan2(x, y);
var mapDistance = Math.Sqrt(x * x + y * y);
var distance = Math.Atan(mapDistance / EarthRadius);
return Center.GetLocation(azimuth, distance);
return GetLocation(x, y, rho, Math.Sin(c));
}
}
}

58
MapControl/Shared/OrthographicProjection.cs
View file

@ -11,7 +11,7 @@ namespace MapControl
/// Spherical Orthographic Projection - AUTO2:42003.
/// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/publication/pp1395), p.148-150.
/// </summary>
public class OrthographicProjection : MapProjection
public class OrthographicProjection : AzimuthalProjection
{
public const string DefaultCrsId = "AUTO2:42003";
@ -22,62 +22,30 @@ namespace MapControl
public OrthographicProjection(string crsId)
{
Type = MapProjectionType.Azimuthal;
CrsId = crsId;
}
public double EarthRadius { get; set; } = Wgs84MeanRadius;
public override Point RelativeScale(double latitude, double longitude)
{
(var cosC, var x, var y) = GetPointValues(latitude, longitude);
var h = cosC; // p.149 (20-5)
return new Point(h, h);
}
public override Point? LocationToMap(double latitude, double longitude)
{
if (Center.Equals(latitude, longitude))
{
return new Point();
}
(var cosC, var x, var y) = GetPointValues(latitude, longitude);
var phi = latitude * Math.PI / 180d;
var phi1 = Center.Latitude * Math.PI / 180d;
var dLambda = (longitude - Center.Longitude) * Math.PI / 180d; // λ - λ0
if (Math.Abs(phi - phi1) > Math.PI / 2d || Math.Abs(dLambda) > Math.PI / 2d)
{
return null;
}
var x = EarthRadius * Math.Cos(phi) * Math.Sin(dLambda); // p.149 (20-3)
var y = EarthRadius * (Math.Cos(phi1) * Math.Sin(phi) -
Math.Sin(phi1) * Math.Cos(phi) * Math.Cos(dLambda)); // p.149 (20-4)
return new Point(x, y);
return cosC >= 0d ? new Point(EarthRadius * x, EarthRadius * y) : null; // p.149 (20-3/4)
}
public override Location MapToLocation(double x, double y)
{
if (x == 0d && y == 0d)
{
return new Location(Center.Latitude, Center.Longitude);
}
var rho = Math.Sqrt(x * x + y * y);
var sinC = rho / EarthRadius; // p.150 (20-19)
x /= EarthRadius;
y /= EarthRadius;
var r2 = x * x + y * y;
if (r2 > 1d)
{
return null;
}
var r = Math.Sqrt(r2); // p.150 (20-18), r=ρ/R
var sinC = r; // p.150 (20-19)
var cosC = Math.Sqrt(1d - r2);
var phi1 = Center.Latitude * Math.PI / 180d;
var cosPhi1 = Math.Cos(phi1);
var sinPhi1 = Math.Sin(phi1);
var phi = Math.Asin(cosC * sinPhi1 + y * sinC * cosPhi1 / r); // p.150 (20-14)
var dLambda = Math.Atan2(x * sinC, r * cosC * cosPhi1 - y * sinC * sinPhi1); // p.150 (20-15)
return new Location(180d / Math.PI * phi, 180d / Math.PI * dLambda + Center.Longitude);
return sinC <= 1d ? GetLocation(x, y, rho, sinC) : null;
}
}
}

35
MapControl/Shared/StereographicProjection.cs
View file

@ -11,7 +11,7 @@ namespace MapControl
/// Spherical Stereographic Projection - AUTO2:97002.
/// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/publication/pp1395), p.157-160.
/// </summary>
public class StereographicProjection : MapProjection
public class StereographicProjection : AzimuthalProjection
{
public const string DefaultCrsId = "AUTO2:97002"; // GeoServer non-standard CRS identifier
@ -22,38 +22,31 @@ namespace MapControl
public StereographicProjection(string crsId)
{
Type = MapProjectionType.Azimuthal;
CrsId = crsId;
}
public double EarthRadius { get; set; } = Wgs84MeanRadius;
public override Point RelativeScale(double latitude, double longitude)
{
(var cosC, var _, var _) = GetPointValues(latitude, longitude);
var k = 2d / (1d + cosC); // p.157 (21-4), k0 == 1
return new Point(k, k);
}
public override Point? LocationToMap(double latitude, double longitude)
{
if (Center.Equals(latitude, longitude))
{
return new Point();
}
(var cosC, var x, var y) = GetPointValues(latitude, longitude);
var k = 2d / (1d + cosC); // p.157 (21-4), k0 == 1
Center.GetAzimuthDistance(latitude, longitude, out double azimuth, out double distance);
var mapDistance = Math.Tan(distance / 2d) * 2d * EarthRadius;
return new Point(mapDistance * Math.Sin(azimuth), mapDistance * Math.Cos(azimuth));
return new Point(EarthRadius * k * x, EarthRadius * k * y); // p.157 (21-2/3)
}
public override Location MapToLocation(double x, double y)
{
if (x == 0d && y == 0d)
{
return new Location(Center.Latitude, Center.Longitude);
}
var rho = Math.Sqrt(x * x + y * y);
var c = 2d * Math.Atan(rho / (2d * EarthRadius)); // p.159 (21-15), k0 == 1
var azimuth = Math.Atan2(x, y);
var mapDistance = Math.Sqrt(x * x + y * y);
var distance = 2d * Math.Atan(mapDistance / (2d * EarthRadius));
return Center.GetLocation(azimuth, distance);
return GetLocation(x, y, rho, Math.Sin(c));
}
}
}

4
MapControl/Shared/TransverseMercatorProjection.cs
View file

@ -83,7 +83,7 @@ namespace MapControl
// λ - λ0
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d;
// ξ'
var xi_ = Math.Atan(t / Math.Cos(dLambda));
var xi_ = Math.Atan2(t, Math.Cos(dLambda));
// η'
var eta_ = Atanh(Math.Sin(dLambda) / Math.Sqrt(1d + t * t));
// ξ
@ -128,7 +128,7 @@ namespace MapControl
d2 * Math.Sin(4d * chi) +
d3 * Math.Sin(6d * chi);
// λ - λ0
var dLambda = Math.Atan(Math.Sinh(eta_) / Math.Cos(xi_));
var dLambda = Math.Atan2(Math.Sinh(eta_), Math.Cos(xi_));
return new Location(
phi * 180d / Math.PI,